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The problem might be weakening motors, but it could be mechanical or electronic.
1: if the power supply to the motors is suffering from variation or instability, then that could make the motors run irregularly.
2: if the motor is pulling the tape onto one reel, the tape is being pulled off of the other reel. If that reel is out-of-round, or is eccentric in mounting (?? dubious), or its brake is not exerting constant resistance, then the 'other reel' would move irregularly and not provide enough resistance to keep the tape up between the two capstan drive wheels.
As for the capstan belt: why did you replace it? And why would it be hard to get positioned right?
Did you clean the areas that the melted-down rubber of the old belt might have touched, or gotten sticky, before replacing the belt?
If not, you will need to replace the new belt yet again, after doing such a cleaning.
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